Internal problem ID [2372]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 40, page 186
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {y^{\prime }-\sin \left (y\right )=\cos \left (x \right )} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = \frac {\pi }{2}\right ] \end {align*}
With the expansion point for the power series method at \(x = \frac {\pi }{2}\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
Order:=4; dsolve([diff(y(x),x)=cos(x)+sin(y(x)),y(1/2*Pi) = 1/2*Pi],y(x),type='series',x=Pi/2);
\[ y \left (x \right ) = \frac {\pi }{2}+\left (x -\frac {\pi }{2}\right )-\frac {1}{2} \left (x -\frac {\pi }{2}\right )^{2}-\frac {1}{6} \left (x -\frac {\pi }{2}\right )^{3}+\operatorname {O}\left (\left (x -\frac {\pi }{2}\right )^{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 22
AsymptoticDSolveValue[{y'[x]==Cos[x]*Sin[y[x]],{y[Pi/2]==Pi/2}},y[x],{x,Pi/2,3}]
\[ y(x)\to \frac {\pi }{2}-\frac {1}{2} \left (x-\frac {\pi }{2}\right )^2 \]